If you're using WordPress MU, I'm affraid you must use the same database, is the way WPMU works. I think there are (or were) plugins to allow you to do that, but the WordPress developers must have designed the MU feature this way for a good reason...

There is a paid-for multidb script by WPMU Dev, it can handle from 16 up to 4096 databases for 100,000+ blogs on the same multisite installation. I currently have it setup with 16 so can't say how messy it will get as you scale up but it depends on your needs.

It works by overwriting some core DB settings in WP, so anything that uses the database with the proper wpdb class won't know the difference - this should be absolutely everything. If you need to tweak your database manually they also provide a tool to find out which database a particular site is stored in.